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An implicit-explicit Eulerian Godunov scheme for compressible flow. (English) Zbl 0817.76038
Summary: A hybrid implicit-explicit scheme is developed for Eulerian hydrodynamics. The hybridization is a continuous switch and operates on each characteristic field separately. The explicit scheme is a version of the second-order Godunov scheme; the implicit method is only first-order accurate in time but leads to a block tridiagonal matrix inversion for efficiency and is unconditionally stable for the case of linear advection. The methodology is described for the cases of linear advection, for nonlinear scalar problems, and for gas dynamics. An important element of our work is the use of a modified Engquist-Osher flux function in place of the Godunov flux. Several numerical results are presented to demonstrate the properties of the method, especially stable numerical shocks at very high CFL numbers and second-order accurate steady states.

76M20 Finite difference methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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